text: The vector approach defines flux density as a vector at a point of space and time prescribed by the investigator. To distinguish this approach, one might speak of the full spherical flux density. In this case, nature tells the investigator what is the magnitude, direction, and sense of the flux density at the prescribed point. For the flux density vector, one may write
  where  denotes the spectral radiance (or specific intensity) at the point  at time  and frequency ,  denotes a variable unit vector with origin at the point ,  denotes an element of solid angle around , and  indicates that the integration extends over the full range of solid angles of a sphere.
  Mathematically, defined as an unweighted integral over the solid angle of a full sphere, the flux density is the first moment of the spectral radiance (or specific intensity) with respect to solid angle. It is not common practice to make the full spherical range of measurements of the spectral radiance (or specific intensity) at the point of interest, as is needed for the mathematical spherical integration specified in the strict definition; the concept is nevertheless used in theoretical analysis of radiative transfer.
  As described below, if the direction of the flux density vector is known in advance because of a symmetry, namely that the radiative field is uniformly layered and flat, then the vector flux density can be measured as the net flux, by algebraic summation of two oppositely sensed scalar readings in the known direction, perpendicular to the layers.
  At a given point in space, in a steady-state field, the vector flux density, a radiometric quantity, is equal to the time-averaged Poynting vector, an electromagnetic field quantity.
  Within the vector approach to the definition, however, there are several specialized sub-definitions. Sometimes the investigator is interested only in a specific direction, for example the vertical direction referred to a point in a planetary or stellar atmosphere, because the atmosphere there is considered to be the same in every horizontal direction, so that only the vertical component of the flux is of interest. Then the horizontal components of flux are considered to cancel each other by symmetry, leaving only the vertical component of the flux as non-zero. In this case some astrophysicists think in terms of the astrophysical flux (density), which they define as the vertical component of the flux (of the above general definition) divided by the number . And sometimes the astrophysicist uses the term Eddington flux to refer to the vertical component of the flux (of the above general definition) divided by the number .